Non-perturbative description of quantum systems / Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov.

Contributor(s): Feranchuk, I. D. (Ilya D.) [author.] | Ivanov, Alexey [author.] | Le, Van-Hoang [author.] | Ulyanenkov, Alexander [author.]
Material type: TextTextSeries: Lecture notes in physics: volume 894.Publisher: Cham : Springer, [2014]Copyright date: ©2014Description: 1 online resource (xv, 362 pages) : illustrations (some color)Content type: text Media type: computer Carrier type: online resourceISBN: 9783319130064; 3319130064Subject(s): Schrödinger equation | Quantum theory -- Mathematics | Mathematical physics | Nuclear physics | Quantum physics (quantum mechanics & quantum field theory) | Science -- Mathematical Physics | Science -- Molecular Physics | Science -- Quantum Theory | Quantum theory -- Mathematics | Schrödinger equation | moleculaire fysica | molecular physics | quantumfysica | quantum physics | fysica | physics | toegepaste wiskunde | applied mathematics | Physics (General) | Fysica (algemeen)Genre/Form: Electronic books. DDC classification: 530.12/4 LOC classification: QC174.26.W28Online resources: Click here to access online
Contents:
Capabilities of approximate methods in quantum theory -- Basics of the operator method -- Applications of OM for one-dimensional systems -- Operator method for quantum statistics -- Quantum systems with several degrees of freedom -- Two-dimensional exciton in magnetic field with arbitrary strength -- Atoms in the external electromagnetic fields -- Many-electron atoms -- Systems with infinite number of degrees of freedom.
Summary: This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
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Includes bibliographical references.

Online resource; title from PDF title page (SpringerLink, viewed January 8, 2015).

Capabilities of approximate methods in quantum theory -- Basics of the operator method -- Applications of OM for one-dimensional systems -- Operator method for quantum statistics -- Quantum systems with several degrees of freedom -- Two-dimensional exciton in magnetic field with arbitrary strength -- Atoms in the external electromagnetic fields -- Many-electron atoms -- Systems with infinite number of degrees of freedom.

This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

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